Well, I'd maintain that your memories 'live' on, but you're no longer there to enjoy them, that's someone else. If that's enough for you, great for you. I personally enjoy having experiences myself.
> What does that even mean?
What does what even mean? To stop existing? Is that a serious question?
I don't understand your point. Are we 'same' (your first sentence) or are we not 'same' (your second sentence)?
My copy and I are different persons because my copy has its own mind in its own brain in its own body. Just like you and I. Why would there be any more reason to think my copy and I are the same self, than to think you and I are the same self?
Do you die every night when you go to sleep?